BRUSSELS — Secretary of Defense Chuck Hagel warned Russia on Thursday to stay out of the turmoil in Ukraine, while NATO defense ministers issued repeated statements meant to show support for the new leadership in Kiev.

“We expect other nations to respect Ukraine’s sovereignty and avoid provocative action,” Mr. Hagel said after the ministers met at NATO headquarters here. “That’s why I’m closely watching Russia’s military exercises along the Ukrainian border, which they just announced yesterday.”

The Russian defense minister, Sergey K. Shoigu, was quoted by state news media saying the exercises were meant to “check combat readiness of armed forces in western and central military districts as well as several branches of the armed forces.” Though General Shoigu did not mention Ukraine, Western officials interpreted the exercises as a warning from Moscow.

Anders Fogh Rasmussen, the secretary general of the NATO, posted Twitter messages Thursday morning warning Russia not to intervene in Ukraine after armed men seized a government headquarters in the Crimea region of southern Ukraine and raised the Russian flag.

“I urge Russia not to take any action that can escalate tension or create misunderstanding,” Mr. Rasmussen wrote on Twitter. “I’m concerned about developments in Crimea.” In a news conference later in the day, Mr. Rasmussen called the Crimea events “dangerous and irresponsible.”

The ministers meeting in Brussels issued similar warnings on Wednesday, saying that the alliance would “continue to support Ukrainian sovereignty and independence, territorial integrity, democratic development and the principle of inviolability of frontiers, as key factors of stability and security in Central and Eastern Europe and on the continent as a whole.”

But it remained unclear how far NATO could go in its admonishments of Russia. Ukraine is not a member of the alliance; the United States tried in 2008 to bring it in, but met with opposition from Germany and France.

The American role in the unfolding events in Ukraine, beyond sending verbal warnings to Russia and supporting financial aid for Ukraine through the International Monetary Fund, is uncertain as well. President Obama has signaled that the bar is high for any American military intervention. Though Mr. Obama is sympathetic to the pro-Western protest movement in Ukraine and to Ukraine’s new leaders, his handling of the crisis has been restrained so far.

Speaking to reporters after the NATO meeting on Ukraine, Mr. Hagel urged Russia “not to take any steps that could be misinterpreted, or lead to miscalculations during a delicate time.” He said he would be talking to General Shoigu soon by telephone.